Bond versus charge disproportionation in the bismuth perovskites

We develop a theory describing a parameter based phase diagram to be associated with materials incorporating skipped valence ions\cite{Varma}. We use a recently developed tight-binding approach for the bismuthates to study the phase diagram exhibiting the crossover from a bond disproportionated (BD) to a charge disproportionated (CD) system in addition to the presence of a new metallic phase. We argue that three parameters determine the underlying physics of the BD-CD crossover when electron correlation effects are small: the hybridization between O-2$p_{\sigma}$ and Bi-6$s$ orbitals ($t_{sp\sigma}$), the charge-transfer energy between Bi-6$s$ and O-a$_{1g}$ molecular orbitals ($\Delta$), and the width of the oxygen sublattice band ($W$). In the BD system, we estimate an effective attractive interaction $U$ between holes on the same O-a$_{1g}$ molecular orbital. Although here we concentrate on the example of the bismuthates, the basic ideas can be directly transferred to other perovskites with negative charge-transfer energy, like ReNiO$_{3}$ (Re: rare-earth element), Ca(Sr)FeO$_{3}$, CsTIF$_{3}$ and CsTlCl$_{3}$.